This needs an update...coming soon in 2009
These are random thoughts and in no particular order.
The temptation by some owners is to go bargain ball and save money. 
Let's get this straight - you need to mix up your roster salary-wise and
obviously you want to try to find the cheap player or rookie who will rise to
stardom this year or get there in future years, but for the most part,  the guys who have large salaries have
them for a reason - they are based on the stats that are used in the games.
In building your list of position players one of the main things to keep in
mind is AB.  You don't build up your game score on Batting Average or
Slugging Pct.  You get it by Hits, Runs, RBI, HR, SB, etc.  Someone
going 2-6 in a game is usually better than someone going 1-1 in a pinch-hitting role
(unless, of course, that hit was a grand slam).  By appearing at the
plate more, the
first player has a greater chance of scoring, getting hits, getting hit by a
pitch, and so on.
That's true even for your bench players.  The ideal people to be on your
bench are real-life starters, since they fill in for you just as any starting
player. 
Many owners ignore the  minor league roster.  I think it's important in a
few ways:
  - You can pick up a million bucks by winning the minor league title (which
    is basically just a rotisserie league using minor league stats only).
 
  - You can pick up future stars and lock them away years in advance of when
    they hit the big leagues and everyone else will know about them.  This
    is also a risk, just like in real life - you may end up picking a career
    minor leaguer or someone who just never cuts it in the bigs.
 
  - Your minor league roster can have anyone making $250,000 or less.  So
    it's also the  ideal place to hold cheap players who are actually playing in the
    big leagues.  This can be important during the season when you get hit
    with an injury on your major league squad.  There's a week lag between
    asking for a free agent and using him in your roster.  By having
    someone available in the minors, you can make that change immediately. 
    (The same holds true in using your taxi squad players.  The benefit of
    the taxi squad is that there is no salary maximum)
 
Think of the taxi squad as a disabled list...but players don't have to be
injured to be on it...so it's more like the extra players on an NFL roster who
don't play each week.
It's obviously a good idea to have guys on your bench who can fill in for
starters.  They will fill in only if they play the position that's
open.   Thus, having a guy who can play  multiple positions can give
you a great deal of flexibility in your bench.  A guy who can play 2B and
SS might eliminate the need for you to carry an additional middle
infielder. (Of course, you'd be SOL if you needed subs at both positions that
day).
Many owners ignored having a good backup catcher this year.  Again if
you're going for a backup, try to find another starter to give you a better shot
of actually having him fill in.  Even when healthy, you've got to figure
that the catcher is the guy on your team who will sit the most.  Then
again, Springfield got hit by a rash of catcher injuries this year - he finally
stopped trying to pick them up and stuck his catcher at the bottom of the lineup
- basically taking an 0-5 and an error every game.  But he ended up with
the best record.   Another approach might be to take the normal
starter and the backup from the same major league team.
Thoughts on building a starting lineup:
  - Build it like you would in real life.  You can try to analyze the
    scoring formula if you really want, but what it comes down to is: Players
    that get on base a lot and score a lot at the top of the lineup. 
    There's a bonus multiplier for total bases and runs for the  top three
    players in your lineup.  For purposes of this game, BB, HBP, and SB
    count as total bases.
 
  - There's a bonus multiplier for RBI for for  positions 3-5.
 
  - If you take the previous two together - it should be clear that your guy
    who hits for average and power should be in spot 3 - unless maybe his
    RBI total is extremely high - then maybe in the cleanup role.
 
  - Players in  positions 8-9 get fewer points for runs, RBI, total bases than
    anyone else - so stick your weak players there.
 
  - If you're plagued by injuries at a position and are getting a lot of
    "Benchwarmer" entries show up in your box score, you might want to
    move the player down to 8 or 9 in the lineup to minimize the effect of the
    0-5 of an Benchwarmer.
 
  - You can hide a poor fielder by putting him at DH - his errors won't count.
 
  - If I had to choose between two guys at DH - one an outfielder and one
    OF-1B, I'd pick the second guy.  Remember that  your DH ends up being
    the first potential position sub.  If he can play multiple positions, that's a
    bonus for you because anyone on the bench can fill in at DH, but you might
    not have someone to fill the open field position on the bench.
 
  - Your bench players will fill in starting at the first slot down to the
    fifth.  It's important to  line them up in the order that you would like
    to see them come into the game regardless of field
    position.  If you've got two outfielder subs,
    make sure the one you want in the most is listed before the other. 
    This also holds for the whole bench.  I might need to use my backup 2B
    a lot.  But if he's not a big hitter or is in a slump, I'd want to
    stick him lower on the bench.  The fill-in process will find him based
    on fielding position if I need him.  But what's more important is that
    anyone can fill in at DH, and I don't want him up higher than anyone hitting
    well and for power so that he isn't used for DH instead of someone else.
 
  - If one of your important hitters is having injury problems, you may not
    want to have him lead off or hit cleanup...whoever subs for him will hit in
    the exact same spot.  London did that in 2000 by actually putting Mark
    McGuire into a lower spot this season (during the time when it was unclear
    whether or not he would play) because whoever was usually filling in for him
    wasn't well-suited for cleanup.
 
In some close games this year, errors made the difference.  I
experimented by taking an error out of the formula and the other team would have
won (many times).  Errors get kind of hidden in the mix, but you should
watch them and see if it changes who you think should start (or be the DH where
the errors won't count). Also you can help yourself by having a bench good
enough to avoid Benchwarmer use.  The Benchwarmer brings with him two 
automatic errors.